16. Effect Modification vs Confounding: Reading Stratified Tables
After this lesson you can
- Define effect modification and contrast it with confounding
- Read a pair of stratified tables and decide whether the strata differ from each other, from the crude, or from neither
- Explain scale dependence and name the ratio or difference scale in every modification claim
- Apply the decision sequence, modification first and confounding second, and write the matching report
- Compute a two-stratum Mantel-Haenszel pooled estimate as a weighted average
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Scheduled for release on November 13, 2026.
A lesson on effect modification, where the effect of an exposure differs across levels of a third variable, and how to tell it apart from confounding in stratified tables. Using the fictional Oakhaven factory, where the solvent's risk ratio is 1.0 under age 50 and 4.0 at 50 and over, it shows why a crude 2.5 describes no one and sets out the order in which to check stratified tables.
Questions and answers
Questions a learner would ask about this lesson. Think through your own answer before you open each one.
- What is effect modification?
Show answer
Effect modification means the effect of an exposure differs across levels of a third variable, which is called the modifier. In the Oakhaven factory, the solvent's risk ratio is 1.0 for workers under 50 and 4.0 for workers 50 and over, so age modifies the solvent's effect. The more precise term is effect measure modification.
- How is effect modification different from confounding?
Show answer
Confounding is a distortion to remove: the strata agree with each other, the crude differs, and you report the adjusted estimate. Effect modification is a finding to report: the strata disagree with each other, and you report each stratum. Adjusting for a modifier erases the very result you found.
- Why does the crude 2.5 in the factory describe no one?
Show answer
The crude risk ratio is 12.5 percent against 5 percent, or 2.5, but 1.0 is true for every younger worker and 4.0 is true for every older worker. The 2.5 is an average of two different effects. Age was balanced across exposure, so there was no confounding, yet there was still no single answer.
- What does it mean to "name the scale"?
Show answer
Effect modification is judged on one scale, either the ratio scale (risk ratio) or the difference scale (risk difference), and the two can disagree. Risks of 10 versus 5 percent and 40 versus 20 percent give the same risk ratio of 2.0 but risk differences of 5 and 20 per 100. So every claim of modification should say which scale it is on, and the stratum risks should be reported so readers can check both.
- In what order should I check stratified tables?
Show answer
Stratify first, then ask whether the strata differ from each other. If they do, report each stratum and stop. Only if they agree do you pool them and compare the pooled estimate with the crude; a difference there means confounding, and you report the pooled estimate with the crude beside it.
Practice quiz
- Question 1Among younger workers the risk ratio is 1.0 and among older workers it is 4.0. This pattern is:
- Question 2In that case, what is the right report?
- Question 3In the modification set, 250 of 2,000 exposed workers and 100 of 2,000 unexposed workers became ill. What is the crude risk ratio?
- Question 4Risks are 10 versus 5 percent in one stratum and 40 versus 20 percent in another. Which statement is correct?
- Question 5What is the first question to ask when reading stratified tables?
- Question 6Which statement about a modifier and confounding is true?
- Question 7Strata risk ratios are 1.5 and 1.5, with stratum sizes of 2,000 and 2,000. What is the Mantel-Haenszel pooled risk ratio?
- Question 8Which question is best answered on the difference scale?
- Question 9What is wrong with taking a plain average of stratum risk ratios to get a pooled estimate?
- Question 10In the role summary, how should each of these be handled: a confounder, a mediator, a modifier?
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Principles of Epidemiology is education in epidemiologic reasoning, not clinical, screening, or policy guidance. Every example is set in the fictional Oakhaven Health District, and every number is invented for teaching.